` Delta ABC` में सिद्ध कीजिए कि -
` cot.A/2 + cot.B/2 + cot. C/2 = (a+b+c)^(2)/(4 Delta ).`

Explanation

` L.H.S = cot.A/2 + cot . B/2 + cot .C/2 `
` = sqrt((s(s-a))/((s-b)(s-c)))+ sqrt((s(s-b))/((s-a)(s-c)))`
` = sqrt((s(s-c))/((s-a)(s-b)))`
` = (sqrt(s)[ (s-a))+(s-b)+(s-c)]/(sqrt((s-a)(s-b)(s-c)))`
` = (sqrt(s)* sqrt(s)[3s-(a+b+c)])/(sqrt(s(s-a)(s-b)(s-c)))`
` = (s* (3s-2s))/Delta = s^(2)/Delta = (4s^(2))/(4Delta)`
` = (2s)^(2)/(4Delta)= (a+b+c)^(2)/(4Delta)= R.H.S`